We conclude, that by picking-up the leading \(\hat{\alpha }_s Y^2\) -term in the exponent of BFKL Green's function (REF ) we have reproduced the well-known “Sudakov” doubly-logarithmic suppression for gluon Unintegrated (or TMD) PDF at \({\bf q}_T^2\ll \mu _Y^2\)  [1]}, [2]}. The Eq. (REF ) also features doubly-logarithmic supression at \(z\ll 1\) , significance of which requires further analysis. The second term in this equation has a subleading power in \(z\) , due to overall factor of \(z\)  in front, while the standard BFKL result for UPDF (REF ) is of leading-power in \(z\) . One could expect something similar to Eq. (REF ) to arise from \(\hat{\alpha }_s Y\) -terms in the solution (REF ).
